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被動隔振體的非線性振動分析
被動隔振體的非線性振動分析
摘要：本文獲得了隔振材料的結構阻尼的數學表達式；利用變形的3次多項式函數表征了隔振材料的非線性剛度；根據被動隔振體的拉格朗日原理導出了由地基振動激勵的計及剛度非線性和結構阻尼的被動隔振體的非線性動力學方程；利用諧波平衡法研究了非線性動力響應，得出了非線性方程的周期解；并對解的穩定性進行了分析，得出了方程周期解的穩定和不穩定區域的分界線方程；對系統進行了頻率響應分析，得出了頻響方程；利用Matlab軟件繪出了穩定和不穩定區域的分界線方程的曲線圖和頻率響應曲線圖;獲得了在進行隔振設計和隔振效果時應該注意的3點結論：
（1） 只有系統的參量位于穩定區范圍時，才有穩定的周期解，在這個區域進行隔振效果比較好；
（2） 被動隔振的剛度非線性和材料阻尼非線性使被動隔振體的頻率響應特性曲線呈硬特性效應，被動隔振體的振動除了存在 的主共振外，還存在 的超諧共振；
（3） 考慮剛度非線性和材料阻尼非線性的被動隔振體的振動產生突跳和滯后現象，當 時其振幅不1定是最大點。
關鍵詞：隔振；結構阻尼；非線性；諧波平衡法
An Analysis on the Nonlinear Oscillation of Passive Vibration Isolator
Abstract: In this essay, the mathematical expression of vibration isolators’ structure damping has been obtained. By using the three-cubed multinomial function, a nonlinear rigidity of vibration isolator has been presented. On the ground of Lagrange Principle, meter and nonlinear rigidity prompted by ground vibration are calculated and the nonlinear kinetic formula is concluded. A research on nonlinear kinetic response has been done by using the method of harmonic balance and gets a periodic result of nonlinear formula. Through an analysis of the stability of the result, a bound equation of stable and instable periodic results of the nonlinear formula is found. A frequency response formula is drawn out by analyzing frequency response of the system. With the help of software Matlab, the curve charts of the bound equation and the frequency response are made. A conclusion as following is drawn with regard to vibration isolation plan and vibration isolation effects.
(1)Only when the parameter of the system is located in the stable bound, can a stable periodic result be attained and only in such a case can a sound effect of vibration isolation be found.
(2)The rigid nonlinearity of the passive vibration isolator and the nonlinearity of the damping make the frequency response curve of passive vibration isolator takes on a rigid characteristic. The main resonance of the passive vibration isolator can be expressed as . Apart from this, there are still superharmonic resonance, including
(3)Given the nonlinear rigidity and the nonlinearity of the damping, which may cause sudden leaps or delay in the vibration, the oscillation amplitude is not necessarily at the highest point even when
Keywords: Vibration isolation; Structural damping; Nonlinear; Method of harmonic balance
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